Schematic geometry of x-ray refraction in a medium for cone-beam DPC-CT.

<p>(<i>x</i>^′,<i>z</i>^′) represents the coordinates of the detector plane. <i>OAC</i> is the mid-plane. <i>D</i> is the distance from the source to the rotation center <i>O</i>. <i>θ</i> represents the view angle under which the data was taken. <i>l</i> is any incident ray in the three dimensional space under <i>θ</i>. <i>P</i> is the line integral of <i>δ</i> along <i>l</i>.</p

Numerical simulation results.

<p>(a) and (b) are the images of the axial mid-plane of the Defrise phantom reconstructed by FDK and AIR algorithms respectively, which correspond to the case with a cone-beam angle of 0^∘. (d) and (e) are the sagittal slices reconstructed by FDK and AIR algorithms respectively, which have a maximum cone-beam angle of 6^∘. Starting from the bottom, the central layer of each disc corresponds to a cone angle of 0^∘, 1.5^∘, 3.0^∘, 4.5^∘ and 6.0^∘. (c) and (f) present the profiles along the red solid lines and the blue dashed lines in (a), (b) and (d), (e). The display grey scale is set to be [0 1.1]×10⁻⁶. The relax coefficient is set to be 0.8 and the number of the overall iterations is 10.</p

3D reconstruction results of the sample.

<p>(a) displays a stack of 2D differential phase contrast projections retrieved from the recorded moiré fringe images by detector. (b),(c) and (d), (e) present the 3D volume rendering and the 3D orthogonal views of the results respectively. (b), (d) and (c), (e) correspond to the results reconstructed by AIR and FDK algorithms respectively. We cut some part of the sample, which is indicated by the red solid curves, to show the internal structure. The relax coefficient is set to be 0.8 and the number of the overall iteration is 10.</p

Comparison of experimental reconstruction results in three typical planes.

<p>(a), (b) and (c) correspond to the axial mid-plane, (d), (e), (f), (d) and (h) to the axial plane with a cone-beam angle of 2.5 ^∘ and (i), (j), (k), (l) and (m) to the sagittal mid-plane. (a), (d), (f), (i) and (k) are reconstructed by FDK algorithm. (b), (e), (g), (j) and (l) are reconstructed by AIR algorithm. (f) and (g) are the regions of interest indicated by the red solid rectangle and the blue dashed rectangle in (d) and (e). (k) and (l) are the regions of interest indicated by the red solid rectangle and the blue dashed rectangle in (i) and (j). (c) presents the profiles along the red solid line and the blue dashed line in (a) and (b), (h) in (f) and (g) and (m) in (k) and (l). The reconstructed value is scaled to [0, 1].</p

The normalized root mean square error in Fig. 3.

<p>The normalized root mean square error in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0117502#pone.0117502.g003" target="_blank">Fig. 3</a>.</p

Implementation procedure of 3D algebraic iteration reconstruction for cone-beam DPC-CT.

<p>Implementation procedure of 3D algebraic iteration reconstruction for cone-beam DPC-CT.</p

Sample positioning and preliminary imaging of PVA contrast agent.

<p>(a) Mouse carcass fixated on the animal bed of a preclinical phase-contrast and dark-field CT scanner. A plastic tube was surgically inserted underneath the peritoneum and some spare volume of the tube for flushing the contrast agent downwards was attached to the right side of the mouse. (b) Transmission image of plastic vials containing water (left) and PVA microbubbles (right). Grey values ranging from 0 to 0.35. (c) Dark-field image of plastic vials containing water (left) and PVA microbubbles (right). Grey values ranging from 0 to 0.75. (d) Visible-light brightfield microscopy image of PVA microbubbles.</p

Measurement of pure PVA bubbles contrast agent.

<p>Grey value scaling is given in brackets. The first column shows the same image with the tube filled with water for three different contrast modalities: (a) transmission [0, 0.9], (d) differential phase [</p><p></p><p></p><p><mo>−</mo></p><p><mi>π</mi><mn>2</mn></p><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>π</mi><mn>2</mn></p><p></p><p></p><p></p>], (g) dark field [0, 1.0]. The second column shows the same image with the tube filled with pure PVA-microbubbles suspension in three different modalities: (b) transmission [0, 0.9], (e) differential phase [<p></p><p></p><p><mo>−</mo></p><p><mi>π</mi><mn>2</mn></p><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>π</mi><mn>2</mn></p><p></p><p></p><p></p>], (h) dark field [0, 1.0]. The third column shows the subtraction of the image with contrast agent (second column) from the image with water (first column) for three different contrast modalities: (c) transmission [0, 0.04], (f) differential phase [<p></p><p></p><p><mo>−</mo></p><p><mi>π</mi><mn>2</mn></p><p></p><p></p><p></p>, <p></p><p></p><p></p><p><mi>π</mi><mn>2</mn></p><p></p><p></p><p></p>], (i) dark field [0, 0.3].<p></p

Transmission electron microscopy image of a PVA microbubble.

<p>The bubble is coated with iron-oxide nanoparticles, manufactured by Surflay nanotec GmbH, Berlin, Germany. Image courtesy Johan Härmark, School of Technology and Health, KTH Royal Institute of Technology, Sweden.</p

Comparison of Histological Slices of Clamped Kidney.

<p>(a) PAS histological slice of the clamped kidney. (b) HE-stained histological slice of the clamped kidney, with a similar slice of the phase-contrast volume (c). For both histology slices a respective zoom view of the inner medulla is given. Scarring and beginning tubular atrophy as well proteinaceous casts could be detected correlating with increasing medullary density in PCI.</p